text: A simple two-element air-spaced lens has nine variables (four radii of curvature, two thicknesses, one airspace thickness, and two glass types).  A multi-configuration lens corrected over a wide spectral band and field of view over a range of focal lengths and over a realistic temperature range can have a complex design volume having over one hundred dimensions.
  Lens optimization techniques that can navigate this multi-dimensional space and proceed to local minima have been studied since the 1940s, beginning with early work by James G. Baker, and later by Feder, Wynne, Glatzel, Grey and others.  Prior to the development of digital computers, lens optimization was a hand-calculation task using trigonometric and logarithmic tables to plot 2-D cuts through the multi-dimensional space. Computerized ray tracing allows the performance of a lens to be modelled quickly, so that the design space can be searched rapidly. This allows design concepts to be rapidly refined. Popular optical design software includes Zemaxs OpticStudio, Synopsyss Code V, and Lambda Research's OSLO. In most cases the designer must first choose a viable design for the optical system, and then numerical modelling is used to refine it. The designer ensures that designs optimized by the computer meet all requirements, and makes adjustments or restarts the process when they do not.